Theoretical investigation on second-order nonlinear optical properties of ruthenium alkynyl–dihydroazulene/vinylheptafulvene complexes

Ru metal acetylide electron donor-acceptor complexes have important applications in the field of nonlinear optics. Herein, in this work, a series of half-sandwich ruthenium-based Cp*(dpe)Ru ([Ru*]) metal complexes with the dihydroazulene/vinylheptafulvene (DHA/VHF) have been investigated by density functional theory (DFT) calculations. The results showed that the position of the [Ru*] acetylide functionality, either para or meta on the phenylene ring to the DHA/VHF core (1c/1o and 2c/2o), and additional a p-phenylene spacer (3c/3o) had a great influence on the second-order nonlinear optical (NLO) responses. The systems 1 and 3 can significantly increased second-order NLO responses compared with system 2. It was attributed to the more obvious charge transfer along y-axis, which is from [Ru*] acetylide functionality to DHA, accompanied by a significant decrease of the transition energy according electron density difference maps and time-dependent DFT calculations. The β_vec values of the open-ring complexes were larger than the corresponding closed-ring complexes owing to the smaller HOMO−LUMO gap in the open-ring complexes. It was also because of the smaller BLA values in open-ring complexes, which had stronger π-conjugation. Especially, the change ratio of β_vec value of system 2 was the largest due to the fact that their charge transfers degree varied greatly. In addition, the frequency-dependent NLO properties of the studied complexes were evaluated at 0.0239 a.u. and 0.0340 a.u. The calculation results demonstrated that the magnitude of the frequency-dependent first hyperpolarizability increased with the increasing frequency. We believe that our present work will be beneficial for further theoretical and experimental studies on large second-order NLO responses of metal complexes.     

Ion–π interaction in impacting the nonlinear optical properties of ion–buckybowl complexes

Ion–buckybowl complexes have received considerable attention in modern chemical research due to its fundamental and practical importance. Herein, we performed density functional theory (DFT) to calculate the geometical structure, binding interactions, dipole moments and the first hyperpolarizabilities (β_tot) of ion–buckybowl complexes (ions are Cl⁻ and Na⁺, buckybowls are quadrannulene, corannulene and sumanene). It is found that the stabilities of ion–buckybowl compounds primarily originate from the interaction energy, which was proved by a new isomerization energy decomposition analysis approach. Plots of reduced density gradient mirror the ion–π weak interaction has been formed between the ions and buckybowls. Significantly, the buckybowl subunits cannot effectively impact the nonlinear optical (NLO), but the kind of ion has marked influence on the second-order NLO responses. The β_tot values of Cl⁻–buckybowl complexes are all larger as compared to that of Na⁺–buckybowl complexes, which is attributed to the large charge-transfer (CT) from Cl⁻ to buckybowl. Our present work will be beneficial for further theoretical and experimental studies on the NLO properties of ion–buckybowl compounds.     

Post-adoption switching behavior for online service substitutes: A perspective of the push–pull–mooring framework

The post-adoption behaviors of online service users are critical performance factors for online service providers. To fill an academic gap that persists regarding bloggers’ switching behavior across online service substitutes, this empirical study investigates which factors affect bloggers who switch social network sites, in an attempt to understand specifically how push, pull, and mooring factors shape their switching intentions. The data to test the hypotheses come from an online survey of 319 bloggers, analyzed using partial least squares techniques. The results confirm positive influences of push and pull effects, a negative influence of mooring effects, and an interactive effect of push and mooring on switching intentions. The push–pull–mooring framework thus is a useful tool for comprehending the competing forces that influence the use of online service substitutes. In particular, perceptions of weak connections and writing anxiety push bloggers away, whereas relative enjoyment and usefulness pull bloggers to social network sites; switching cost and past experience also inhibit a change. These findings offer key insights and implications for the competitive strategy choices of online service providers.     

New predictor–corrector methods of second-order for solving nonlinear equations

In this paper, two predictor–corrector methods are proposed for solving nonlinear equations by combining the fuzzy parameterized method with the exponential iterative method and the regula falsi method. The parameter values are determined by a Γ-fuzzy number in the iterative procedure. These two methods present attractive features such as being independent of the initial values, or being adaptive for the iterative formulas. They are verified to also be quadratically convergent. Compared with the previously well-known methods, numerical experiments show that new predictor–corrector methods are effective.     

An efficient split-step quasi-compact finite difference method for the nonlinear fractional Ginzburg–Landau equations

In this paper, we propose a split-step quasi-compact finite difference method to solve the nonlinear fractional Ginzburg–Landau equations both in one and two dimensions. The original equations are split into linear and nonlinear subproblems. The Riesz space fractional derivative is approximated by a fourth-order fractional quasi-compact method. Furthermore, an alternating direction implicit scheme is constructed for the two dimensional linear subproblem. The unconditional stability and convergence of the schemes are proved rigorously in the linear case. Numerical experiments are performed to confirm our theoretical findings and the efficiency of the proposed method.     

Hybrid algorithms for the twin–screw extrusion configuration problem

The twin-screw configuration problem (TSCP) arises in the context of polymer processing, where twin-screw extruders are used to prepare polymer blends, compounds or composites. The goal of the TSCP is to define the configuration of a screw from a given set of screw elements. The TSCP can be seen as a sequencing problem as the order of the screw elements on the screw axis has to be defined. It is also inherently a multi-objective problem since processing has to optimize various conflicting parameters related to the degree of mixing, shear rate, or mechanical energy input among others. In this article, we develop hybrid algorithms to tackle the bi-objective TSCP. The hybrid algorithms combine different local search procedures, including Pareto local search and two phase local search algorithms, with two different population-based algorithms, namely a multi-objective evolutionary algorithm and a multi-objective ant colony optimization algorithm. The experimental evaluation of these approaches shows that the best hybrid designs, combining Pareto local search with a multi-objective ant colony optimization approach, outperform the best algorithms that have been previously proposed for the TSCP.     

A new second-order accurate time discretization method for the nonlinear cubic Schrödinger equation

A new second-order accurate semi-analytical time discretization method is introduced for the numerical solution of the one-dimensional nonlinear cubic Schrödinger equation. This method is based on the combination of the method of lines, Crank–Nicolson method, Newton method and Lanczos’ Tau method. It is a self-starting averaged two-time-level scheme that has proved to be stable, accurate and energy conservative for long time integration periods. At each time level, approximate solutions are sought on a segmented spatial interval as finite expansions in terms of a given orthogonal polynomial basis mapped appropriately onto each spatial subsegment. We have carried out numerical simulation concerning several cases for the propagation, collision and the bound states of solitons. Accurate results have been obtained using Chebyshev and Legendre polynomials. These results are well comparable with other published results obtained by the use of various standard numerical methods.     

A second-order linearized finite difference scheme for the generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation

The purpose of this paper is to study the numerical simulation of the generalized Fisher–Kolmogorov–Petrovskii–Piskunov equation. After introducing a new variable, the integro-differential equation is transformed into an equivalent coupled system of first-order differential equations. A second-order accurate difference scheme is constructed for the new system of equations, which is proved to be local uncoupled by separation of variables. It is also proved that the scheme is uniquely solvable and second-order convergent in both time and space in L ₂-norm. A numerical example is given to demonstrate the theoretical results.     

Solvent effect on the nonlinear optical properties of para-nitroaniline studied by Langevin dipoles–Monte Carlo (LD/MC) approach

Polarizabilities and hyperpolarizabilities and their frequency dispersions are calculated for para-nitroaniline in the water solvent using Langevin dipoles–Monte Carlo (LD/MC) approach. The sum-over-states formalism is used to calculate individual components of linear and nonlinear polarizability tensors for para-nitroaniline. The calculated values of hyperpolarizability including the solvent effect are compared with experimental results from solution phase EFISH measurements.     

Optimal vorticity accuracy in an efficient velocity–vorticity method for the 2D Navier–Stokes equations

We study a velocity–vorticity scheme for the 2D incompressible Navier–Stokes equations, which is based on a formulation that couples the rotation form of the momentum equation with the vorticity equation, and a temporal discretization that stably decouples the system at each time step and allows for simultaneous solving of the vorticity equation and velocity–pressure system (thus if special care is taken in its implementation, the method can have no extra cost compared to common velocity–pressure schemes). This scheme was recently shown to be unconditionally long-time \(H^1\) stable for both velocity and vorticity, which is a property not shared by any common velocity–pressure method. Herein, we analyze the scheme’s convergence, and prove that it yields unconditional optimal accuracy for both velocity and vorticity, thus making it advantageous over common velocity–pressure schemes if the vorticity variable is of interest. Numerical experiments are given that illustrate the theory and demonstrate the scheme’s usefulness on some benchmark problems.     

Application of input — State of the system transformation for linearization of some nonlinear generators

The paper presents an application of the transformation input — state of the system, built on the basis of elements of the theory of differential geometry allowing linearization of a certain class of nonlinear generators to a linear form. The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included.     

A hybrid optical–mechanical calibration procedure for the Scalable-SPIDAR haptic device

In this research, a simple, yet, efficient calibration procedure is presented in order to improve the accuracy of the Scalable-SPIDAR haptic device. The two-stage procedure aims to reduce discrepancies between measured and actual values. First, we propose a new semi-automatic procedure for the initialization of the haptic device. To perform this initialization with a high level of accuracy, an infrared optical tracking device was used. Furthermore, audio and haptic cues were used to guide the user during the initialization process. Second, we developed two calibration methods based on regression techniques that effectively compensate for the errors in tracked position. Both neural networks and support vector regression methods were applied to calibrate the position errors present in the haptic device readings. A comparison between these two regression methods was carried out to show the underlying algorithm and to indicate the inherent advantages and limitations for each method. Initial evaluation of the proposed procedure indicated that it is possible to improve accuracy by reducing the Scalable-SPIDAR’s average absolute position error to about 6 mm within a 1 m × 1 m × 1 m workspace.     

Evolution of structure,stability, and nonlinear optical properties of the heterodinuclear CNLin (n = 1–10) clusters

The lowest-energy structures and stabilities of the heterodinuclear clusters, CNLi_n (n = 1–10) and relevant CNLi_n⁺ (n = 1–10) cations, are studied using the density functional theory with the 6-311 + G(3df) basis set. The CNLi₆ and CNLi₅⁺ clusters are the first three-dimensional ones in the CNLi_n^0/+ series, respectively, and the CN group always caps the Li_n^0/+ moiety in the CNLi_n^0/+ (n = 1–9) configurations. The CN triple bond is found to be completely cleaved in the CNLi₁₀^0/+ clusters where the C and N atoms are bridged by two Li atoms. The CNLi_n (n = 2–10) clusters are hyperlithiated molecules with delocalized valence electrons and consequently possess low VIP values of 3.780–5.674 eV. Especially, the CNLi₈ and CNLi₁₀ molecules exhibit lower VIPs than that of Cs atom and can be regarded as heterobinuclear superalkali species. Furthermore, these two superalkali clusters show extraordinarily large first hyperpolarizabilities of 19,423 and 42,658 au, respectively. For the CNLi_n⁺ cationic species, the evolution of the energetic and electronic properties with the cluster size shows a special stability for CNLi₂⁺.     

An atomistic geometrical model of the B-DNA configuration for DNA–radiation interaction simulations

In this paper, an atomistic geometrical model for the B-DNA configuration is explained. This model accounts for five organization levels of the DNA, up to the 30 nm chromatin fiber. However, fragments of this fiber can be used to construct the whole genome. The algorithm developed in this work is capable to determine which is the closest atom with respect to an arbitrary point in space. It can be used in any application in which a DNA geometrical model is needed, for instance, in investigations related to the effects of ionizing radiations on the human genetic material. Successful consistency checks were carried out to test the proposed model.     

Bio‐optical properties and estimation of the optically active substances in Lake Tianmuhu in summer

Bio‐optical properties in an optically complex and biologically productive region of Lake Tianmuhu were determined in three cruises from June to August 2006. The concentrations of three optically active substances, tripton C _Tripton (calculated from total suspended matter and chlorophyll‐a (Chla) and phaeophytin‐a (Pa)), phytoplankton pigment C _Chla+Pa , and chromophoric dissolved organic matter (CDOM) a _CDOM(440), were predicted from the estimated irradiance reflectance based on in situ measurements and laboratory analyses. The total relative contributions of phytoplankton, tripton, CDOM and pure water over the range of photosynthetically active radiation (PAR) (400–700 nm) were 36.1%, 24.2%, 15.9% and 23.8%, respectively. The dominant contribution of phytoplankton to the total absorption was due to high phytoplankton pigment concentration. The range and variation in irradiance reflectance and diffuse attenuation coefficient derived from a bio‐optical model, based on inherent optical properties, compared well with the measured variability. A reasonably strong relationship (R² = 0.92) was observed between irradiance reflectance at 780 nm R(780) and C _Tripton. For our data set, the best algorithm for C _Chla+Pa used the three‐band reflectance model [R ^?1(688)?R ^?1(717)]×R(747). The a _CDOM(440) could be estimated using the ratio of irradiance reflectance R(682)/R(555). The retrieval accuracy (R²) of tripton, phytoplankton pigment and CDOM was 0.92, 0.87 and 0.91, respectively, while the rms. error was 0.90 mg l^?1 (18.2%), 3.27 µg l^?1 (14.8%) and 0.073 m^?1 (15.3%), respectively. Estimation of the concentrations of the three optically active substances was reasonably accurate based on inherent optical properties measurement.     

Asymptotic properties of the space–time adaptive numerical solution of a nonlinear heat equation

We consider the fully adaptive space–time discretization of a class of nonlinear heat equations by Rothe’s method. Space discretization is based on adaptive polynomial collocation which relies on equidistribution of the defect of the numerical solution, and the time propagation is realized by an adaptive backward Euler scheme. From the known scaling laws, we infer theoretically the optimal grids implying error equidistribution, and verify that our adaptive procedure closely approaches these optimal grids.     

L4–L5 compression and anterior/posterior joint shear forces in cabin attendants during the initial push/pull actions of airplane meal carts

The aim of the present study was to assess the acute low back load of cabin attendants during cart handling and to identify working situations which present the highest strain on the worker. In a setup, 17 cabin attendants (ten females and seven males) pushed, pulled and turned a 20 kg standard meal cart (L: 0.5 m × W: 0.3 m × H: 0.92 m) loaded with extra 20 kg and 40 kg, respectively on two different surfaces (carpet and linoleum) and at three floor inclinations (−2°, 0° and +2°). Two force transducers were mounted as handles. Two-dimensional movement analysis was performed and a 4D WATBAK modelling tool was used to calculate the acute L4–L5 load.     

Derivation of the multisymplectic Crank–Nicolson scheme for the nonlinear Schrödinger equation

The Crank–Nicolson scheme as well as its modified schemes is widely used in numerical simulations for the nonlinear Schrödinger equation. In this paper, we prove the multisymplecticity and symplecticity of this scheme. Firstly, we reconstruct the scheme by the concatenating method and present the corresponding discrete multisymplectic conservation law. Based on the discrete variational principle, we derive a new variational integrator which is equivalent to the Crank–Nicolson scheme. Therefore, we prove the multisymplecticity again from the Lagrangian framework. Symplecticity comes from the proper discrete Hamiltonian structure and symplectic integration in time. We also analyze this scheme on stability and convergence including the discrete mass conservation law. Numerical experiments are presented to verify the efficiency and invariant-preserving property of this scheme. Comparisons with the multisymplectic Preissmann scheme are made to show the superiority of this scheme.